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Dec 02, 2014

- 1. Public Key Cryptographyand the RSA Algorithm Cryptography and Network Security by William Stallings Lecture slides by Lawrie Brown Edited by Dick Steflik

2. Private-Key Cryptography

- traditionalprivate/secret/single keycryptography usesonekey

- Key is shared by both sender and receiver

- if the key is disclosed communications are compromised

- also known assymmetric , both parties are equal

- hence does not protect sender from receiver forging a message & claiming is sent by sender

3. Public-Key Cryptography

- probably most significant advance in the 3000 year history of cryptography

- usestwokeys a public key and a private key

- asymmetricsince parties arenotequal

- uses clever application of number theory concepts to function

- complementsrather thanreplaces private key cryptography

4. Public-Key Cryptography

- public-key/two-key/asymmetriccryptography involves the use oftwokeys:

- apublic-key , which may be known by anybody, and can be used toencrypt messages , andverify signatures

- aprivate-key , known only to the recipient, used todecrypt messages , andsign(create)signatures

- isasymmetricbecause

- those who encrypt messages or verify signaturescannotdecrypt messages or create signatures

5. Public-Key Cryptography 6. Why Public-Key Cryptography?

- developed to address two key issues:

- key distribution how to have secure communications in general without having to trust a KDC with your key

- digital signatures how to verify a message comes intact from the claimed sender

- public invention due to Whitfield Diffie & Martin Hellman at Stanford U. in 1976

- known earlier in classified community

7. Public-Key Characteristics

- Public-Key algorithms rely on two keys with the characteristics that it is:

- computationally infeasible to find decryption key knowing only algorithm & encryption key

- computationally easy to en/decrypt messages when the relevant (en/decrypt) key is known

- either of the two related keys can be used for encryption, with the other used for decryption (in some schemes)

8. Public-Key Cryptosystems 9. Public-Key Applications

- can classify uses into 3 categories:

- encryption/decryption(provide secrecy)

- digital signatures(provide authentication)

- key exchange(of session keys)

- some algorithms are suitable for all uses, others are specific to one

10. Security of Public Key Schemes

- like private key schemes brute forceexhaustive searchattack is always theoretically possible

- but keys used are too large (>512bits)

- security relies on alarge enoughdifference in difficulty betweeneasy(en/decrypt) andhard(cryptanalyse) problems

- more generally thehardproblem is known, its just made too hard to do in practise

- requires the use ofvery large numbers

- hence isslowcompared to private key schemes

11. RSA

- by Rivest, Shamir & Adlemanof MIT in 1977

- best known & widely used public-key scheme

- based on exponentiation in a finite (Galois) field over integers modulo a prime

- nb. exponentiation takes O((log n) 3 ) operations (easy)

- uses large integers (eg. 1024 bits)

- security due to cost of factoring large numbers

- nb. factorization takes O(elog n log log n ) operations (hard)

12. RSA Key Setup

- each user generates a public/private key pair by:

- selecting two large primes at random -p, q

- computing their system modulusN=p.q

- note(N)=(p-1)(q-1)

- selecting at random the encryption keye

- where 1< e

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